how to solve FDM on second-order partial differential equations in 3D

[mumu-1005]

u_t = a^2 (u_xx + u_yy + u_zz)

https://en.wikipedia.org/wiki/Heat_equation

[david-zwicker]

The heat equation is equivalent to the diffusion equation, so you can look at these examples.

[mumu-1005]

a independent system including two cubic coupled by one cylindrical

[david-zwicker]

It's not clear to me what you're asking. Could you give more details?

[mumu-1005]

the system like this

[david-zwicker]

I'm still not sure which equation you're trying to solve, but py-pde is not designed to handle complex geometries. You might want to look into finite element or finite volume methods.

[mumu-1005]

Get it! Thank you very much!